Yes it pretty much is the only reason he done it. He didn't have to kill Torygg in order to gain support for his rebellion, The banning of the worship of Talos, The Empire letting the Thalmor enforce the WGC, and the Thalmor dragging people out of their homes at night was more then enough already to get half the country behind him. No, Ulfric killed him just because he could....just to prove to himself and whoever that he is the strong one.
Ulfric won the duel in a cowardly way anyways, he couldn't even fight Torygg "man to man" "blade to blade" instead he had to resort to using the Thu'um to get the upper hand.
The Way of The Voice is sanctioned by The Nine Divines as the correct and only acceptable use of the Thu'um by individuals that are NOT Dragonborn. Arngeir tells you that a Dragonborn is exempted from the rules of the Way of the Voice.
Are you famliair with the lore of Jurgen Windcaller...he was the most powerful of the Ancient Nord Tongues....him and his fellow voices users and their army were annihilated at the Battle of Red Mountain by the Tribunal....Windcaller couldn't figure out why Strong Voices failed.....it was enough to fend off Alduin, but couldn't beat the Tribunal....
7 years later Windcaller realized the Divines punished the Nords for their arrogant militant use of the Voice for Martial exploits...the Divines gave them the ability to shout like Dragons just to defeat Alduin, who wanted to rule the world instead of just endling kalpa's, and to honor the Divines.
When Windcaller told the other Nords about this, 17 of the strongest tongues of the first era challenged Windcaller to combat in dispute. Windcaller swallowed the shouts of all 17 tongues for 3 days until they all lay exhausted....they later became his pupils.
How do you suppose Windcaller, a non-dragonborn, was able to do this? because when the Divines revealed to him why he lost at Red Mountain, they gave him the ability to do this to pound home the point to the Nords that the Voice is NOT meant to be used as a tool in martial exploits.
Since Ulfric is not Dragonborn, not only has be broken the rules of the Greybeards, whom he swore to follow a path, but he has also broken the decree of the 9 Divines on proper use of the Voice. Dragonborn are exempt from the rules of the Way of the Voice, others are not.
Had Ulfric slayed Torygg in a fair fight without using the Th"um, then I may be more inclined to agree with you, but Ulfric just killed Torygg to inflate and stroke his huge ego.....its all about him wanting to be high king....if he cared about Skyrim as much as he says he does, then even if Elisif was named Queen by the moot he would support her (if the cloaks win the civil war), but Ulfric would never support an independent skyrim with someone else as high king, nope, it has to be his way or no way.
Honestly though, Ulfric using the Th"um to kill Torygg is like bringing an Uzi to a sword fight...its not even fair in the least....it would be like bringing a knife to a gun fight...you know whos going to win their...it was cowardly the way Ulfric did it....he should have been a man and fought Torggg blade to blade without using the Th"um.....atleast then I could give Ulfric the nod that he won the fight fair...its just my opinion.
Don't get me wrong though, Tullius is just a cold, insensitive, pompous idiot. its not like the Empire is much better.